Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 197
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To keep things interesting I am posting another challenge:
There are truth-tellers and liars on the island. The former always tell the truth, the latter always lie. Every inhabitant of the island lives in a four-storey house. All the islanders took part in a sociological survey. To the question "Do you live on the ground floor?" 40% of the residents answered "yes". A similar question about the first floor was answered affirmatively by 30%, about the third floor by 50% and about the fourth floor by 0%. What percentage of islanders actually live on the ground floor?
The weight is 3. The task can be found here.
To keep things interesting, I am posting another challenge:
There are truth-tellers and liars on the island. The former always tell the truth, the latter always lie. Each inhabitant of the island lives in a four-storey house. All the islanders took part in a sociological survey. To the question "Do you live on the ground floor?" 40% of the residents answered "yes". A similar question about the first floor was answered affirmatively by 30%, about the third floor by 50% and about the fourth floor by 0%. What percentage of islanders actually live on the ground floor?
The weight is 3. The task can be found here.
Liars are 10%.
Liars are 10%.
There are 13 candles in the magical candlestick, arranged in a circle. Some of them are lit. The magic is that if you light or extinguish one candle, two neighbouring candles will also change their state: the unlit ones will light up and the burning ones will go out. Is it always possible to get all the candles to burn at the same time?
Weight - 3. The task is here.
The problem seems to be solved only when the number of candles is a multiple of 3, i.e. either 12 or 15.
With 13 candles there is no solution.
The problem seems to be solved only when the number of candles is a multiple of 3, i.e. either 12 or 15.
With 13 candles there is no solution.
There are nuances. Think again.
In principle the moderator has already admitted that I solved it, but not very nice. After a suggestion to look for a more elegant solution, I agreed.
There are nuances. Think again.
In principle, the moderator has already acknowledged that I have solved it, but not very nicely. After a suggestion to look for a more elegant solution, I agreed.
It is possible if in the first arrangement one of 13 candles is already burning (or 4 or 7 or 10 in a row), then there is a simple solution. But if all the candles are extinguished at the beginning, it's unlikely.... There must be an extra trick here, as the initial condition is too vague: "As in life - anything is possible! "